Application of Kohonen's self-organizing feature map algorithm to cortical maps of orientation and direction preference

Cortical maps of orientation preference in cats, ferrets and monkeys contain numerous half-rotation point singularities. Experimental data have shown that direction preference also has a smooth representation in these maps, with preferences being for the most part orthogonal to the axis of preferred orientation. As a result, the orientation singularities induce an extensive set of linear fractures in the direction map. These fractures run between and connect nearby point orientation singularities. Their existence appears to pose a puzzle for theories that postulate that cortical maps maximize continuity of representation, because the fractures could be avoided if the orientation map contained full-rotation singularities. Here we show that a dimension-reduction model of cortical map formation, which implements principles of continuity and completeness, produces an arrangement of linear direction fractures connecting point orientation singularities which is similar to that observed experimentally. We analyse the behaviour of this model and suggest reasons why the model maps contain half-rotation rather than full-rotation orientation singularities.     

A spherical model for orientation and spatial-frequency tuning in a cortical hypercolumn

A theory is presented of the way in which the hypercolumns in primary visual cortex (V1) are organized to detect important features of visual images, namely local orientation and spatial-frequency. Given the existence in V1 of dual maps for these features, both organized around orientation pinwheels, we constructed a model of a hypercolumn in which orientation and spatial-frequency preferences are represented by the two angular coordinates of a sphere. The two poles of this sphere are taken to correspond, respectively, to high and low spatial-frequency preferences. In Part I of the paper, we use mean-field methods to derive exact solutions for localized activity states on the sphere. We show how cortical amplification through recurrent interactions generates a sharply tuned, contrast-invariant population response to both local orientation and local spatial frequency, even in the case of a weakly biased input from the lateral geniculate nucleus (LGN). A major prediction of our model is that this response is non-separable with respect to the local orientation and spatial frequency of a stimulus. That is, orientation tuning is weaker around the pinwheels, and there is a shift in spatial-frequency tuning towards that of the closest pinwheel at non-optimal orientations. In Part II of the paper, we demonstrate that a simple feed-forward model of spatial-frequency preference, unlike that for orientation preference, does not generate a faithful representation when amplified by recurrent interactions in V1. We then introduce the idea that cortico-geniculate feedback modulates LGN activity to generate a faithful representation, thus providing a new functional interpretation of the role of this feedback pathway. Using linear filter theory, we show that if the feedback from a cortical cell is taken to be approximately equal to the reciprocal of the corresponding feed-forward receptive field (in the two-dimensional Fourier domain), then the mismatch between the feed-forward and cortical frequency representations is eliminated. We therefore predict that cortico-geniculate feedback connections innervate the LGN in a pattern determined by the orientation and spatial-frequency biases of feed-forward receptive fields. Finally, we show how recurrent cortical interactions can generate cross-orientation suppression.     

The influence of cortical feature maps on the encoding of the orientation of a short line

The inhomogeneous distribution of the receptive fields of cortical neurons influences the cortical representation of the orientation of short lines seen in visual images. We construct a model of the response of populations of neurons in the human primary visual cortex by combining realistic response properties of individual neurons and cortical maps of orientation and location preferences. The encoding error, which characterizes the difference between the parameters of a visual stimulus and their cortical representation, is calculated using Fisher information as the square root of the variance of a statistically efficient estimator. The error of encoding orientation varies considerably with the location and orientation of the short line stimulus as modulated by the underlying orientation preference map. The average encoding error depends only weakly on the structure of the orientation preference map and is much smaller than the human error of estimating orientation measured psychophysically. From this comparison we conclude that the actual mechanism of orientation perception does not make efficient use of all the information available in the neuronal responses and that it is the decoding of visual information from neuronal responses that limits psychophysical performance. Action Editor: Terrence Sejnowski     

Combined Hebbian development of geniculocortical and lateral connectivity in a model of primary visual cortex

We present a network model of visual map development in layer 4 of primary visual cortex. Our model comprises excitatory and inhibitory spiking neurons. The input to the network consists of correlated spike trains to mimick the activity of neurons in the lateral geniculate nucleus (LGN). An activity-driven Hebbian learning mechanism governs the development of both the network's lateral connectivity and feedforward projections from LGN to cortex. Plasticity of inhibitory synapses has been included into the model so as to control overall cortical activity. Even without feedforward input, Hebbian modification of the excitatory lateral connections can lead to the development of an intracortical orientation map. We have found that such an intracortical map can guide the development of feedforward connections from LGN to cortical simple cells so that the structure of the final feedforward orientation map is predetermined by the intracortical map. In a scenario in which left- and right-eye geniculocortical inputs develop sequentially one after the other, the resulting maps are therefore very similar, provided the intracortical connectivity remains unaltered. This may explain the outcome of so-called reverse lid-suture experiments, where animals are reared so that both eyes never receive input at the same time, but the orientation maps measured separately for the two eyes are nevertheless nearly identical. Received: 20 December 1999 / Accepted in revised form: 9 June 2000     

Parsimony,Exhaustivity and Balanced Detection in Neocortex

The layout of sensory brain areas is thought to subtend perception. The principles shaping these architectures and their role in information processing are still poorly understood. We investigate mathematically and computationally the representation of orientation and spatial frequency in cat primary visual cortex. We prove that two natural principles, local exhaustivity and parsimony of representation, would constrain the orientation and spatial frequency maps to display a very specific pinwheel-dipole singularity. This is particularly interesting since recent experimental evidences show a dipolar structures of the spatial frequency map co-localized with pinwheels in cat. These structures have important properties on information processing capabilities. In particular, we show using a computational model of visual information processing that this architecture allows a trade-off in the local detection of orientation and spatial frequency, but this property occurs for spatial frequency selectivity sharper than reported in the literature. We validated this sharpening on high-resolution optical imaging experimental data. These results shed new light on the principles at play in the emergence of functional architecture of cortical maps, as well as their potential role in processing information.     

Pairing-induced changes of orientation maps in cat visual cortex.

We have studied the precise temporal requirements for plasticity of orientation preference maps in kitten visual cortex. Pairing a brief visual stimulus with electrical stimulation in the cortex, we found that the relative timing determines the direction of plasticity: a shift in orientation preference toward the paired orientation occurs if the cortex is activated first visually and then electrically; the cortical response to the paired orientation is diminished if the sequence of visual and electrical activation is reversed. We furthermore show that pinwheel centers are less affected by the pairing than the pinwheel surround. Thus, plasticity is not uniformly distributed across the cortex, and, most importantly, the same spike time-dependent learning rules that have been found in single-cell in vitro studies are also valid on the level of cortical maps.     

Shunting inhibition, a silent step in visual cortical computation

Brain computation, in the early visual system, is often considered as a hierarchical process in which features extracted in a given sensory relay are not present in previous stages of integration. In particular, orientation preference and its fine tuning selectivity are functional properties shared by most cortical cells and they are not observed at the preceding geniculate stage. A classical problem is identifying the mechanisms and circuitry underlying these computations. Several organizational principles have been proposed, giving different weights to the feedforward thalamocortical drive or to intracortical recurrent architectures. Within this context, an important issue is whether intracortical inhibition is fundamental for the genesis of stimulus selectivity, or rather normalizes spike response tuning with respect to other features such as stimulus strength or contrast, without influencing the selectivity bias and preference expressed in the excitatory input alone. We review here experimental observations concerning the presence or absence of inhibitory input evoked by non-preferred orientation/directions. Intracellular current clamp and voltage clamp recordings are analyzed in the light of new methods allowing us (1) to increase the visibility of inhibitory input, and (2) to continuously measure the visually evoked dynamics of input conductances. We conclude that there exists a diversity of synaptic input combinations generating the same profile of spike-based orientation selectivity, and that this diversity most likely reflects anatomical non-homogeneities in input sampling provided by the local context of the columnar and lateral intracortical network in which the considered cortical cell is embedded.     

Coarse-grained reduction and analysis of a network model of cortical response: I. Drifting grating stimuli

We present a reduction of a large-scale network model of visual cortex developed by McLaughlin, Shapley, Shelley, and Wielaard. The reduction is from many integrate-and-fire neurons to a spatially coarse-grained system for firing rates of neuronal subpopulations. It accounts explicitly for spatially varying architecture, ordered cortical maps (such as orientation preference) that vary regularly across the cortical layer, and disordered cortical maps (such as spatial phase preference or stochastic input conductances) that may vary widely from cortical neuron to cortical neuron. The result of the reduction is a set of nonlinear spatiotemporal integral equations for phase-averaged firing rates of neuronal subpopulations across the model cortex, derived asymptotically from the full model without the addition of any extra phenomological constants. This reduced system is used to study the response of the model to drifting grating stimuli—where it is shown to be useful for numerical investigations that reproduce, at far less computational cost, the salient features of the point-neuron network and for analytical investigations that unveil cortical mechanisms behind the responses observed in the simulations of the large-scale computational model. For example, the reduced equations clearly show (1) phase averaging as the source of the time-invariance of cortico-cortical conductances, (2) the mechanisms in the model for higher firing rates and better orientation selectivity of simple cells which are near pinwheel centers, (3) the effects of the length-scales of cortico-cortical coupling, and (4) the role of noise in improving the contrast invariance of orientation selectivity.     

Coordinated Optimization of Visual Cortical Maps (I) Symmetry-based Analysis

In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of orientation columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about a hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference. From basic symmetry assumptions we obtain a comprehensive phenomenological classification of possible inter-map coupling energies and examine representative examples. We show that each individual coupling energy leads to a different class of OP solutions with different correlations among the maps such that inferences about the optimization principle from map layout appear viable. We systematically assess whether quantitative laws resembling experimental observations can result from the coordinated optimization of orientation columns with other feature maps.     

Generalized spin models for coupled cortical feature maps obtained by coarse graining correlation based synaptic learning rules

We derive generalized spin models for the development of feedforward cortical architecture from a Hebbian synaptic learning rule in a two layer neural network with nonlinear weight constraints. Our model takes into account the effects of lateral interactions in visual cortex combining local excitation and long range effective inhibition. Our approach allows the principled derivation of developmental rules for low-dimensional feature maps, starting from high-dimensional synaptic learning rules. We incorporate the effects of smooth nonlinear constraints on net synaptic weight projected from units in the thalamic layer (the fan-out) and on the net synaptic weight received by units in the cortical layer (the fan-in). These constraints naturally couple together multiple feature maps such as orientation preference and retinotopic organization. We give a detailed illustration of the method applied to the development of the orientation preference map as a special case, in addition to deriving a model for joint pattern formation in cortical maps of orientation preference, retinotopic location, and receptive field width. We show that the combination of Hebbian learning and center-surround cortical interaction naturally leads to an orientation map development model that is closely related to the XY magnetic lattice model from statistical physics. The results presented here provide justification for phenomenological models studied in Cowan and Friedman (Advances in neural information processing systems 3, 1991), Thomas and Cowan (Phys Rev Lett 92(18):e188101, 2004) and provide a developmental model realizing the synaptic weight constraints previously assumed in Thomas and Cowan (Math Med Biol 23(2):119–138, 2006).     

Large-scale modeling of the primary visual cortex: influence of cortical architecture upon neuronal response.

A large-scale computational model of a local patch of input layer 4 [Formula: see text] of the primary visual cortex (V1) of the macaque monkey, together with a coarse-grained reduction of the model, are used to understand potential effects of cortical architecture upon neuronal performance. Both the large-scale point neuron model and its asymptotic reduction are described. The work focuses upon orientation preference and selectivity, and upon the spatial distribution of neuronal responses across the cortical layer. Emphasis is given to the role of cortical architecture (the geometry of synaptic connectivity, of the ordered and disordered structure of input feature maps, and of their interplay) as mechanisms underlying cortical responses within the model. Specifically: (i) Distinct characteristics of model neuronal responses (firing rates and orientation selectivity) as they depend upon the neuron's location within the cortical layer relative to the pinwheel centers of the map of orientation preference; (ii) A time independent (DC) elevation in cortico-cortical conductances within the model, in contrast to a "push-pull" antagonism between excitation and inhibition; (iii) The use of asymptotic analysis to unveil mechanisms which underly these performances of the model; (iv) A discussion of emerging experimental data. The work illustrates that large-scale scientific computation--coupled together with analytical reduction, mathematical analysis, and experimental data, can provide significant understanding and intuition about the possible mechanisms of cortical response. It also illustrates that the idealization which is a necessary part of theoretical modeling can outline in sharp relief the consequences of differing alternative interpretations and mechanisms--with final arbiter being a body of experimental evidence whose measurements address the consequences of these analyses.     

Origin of orientation tuning in the visual cortex.

The results of recent experiments have thrown new light on the neuronal connections underlying orientation-selective responses in the primary visual cortex of adult animals. The pattern of afferent input from the lateral geniculate nucleus to the cortex appears to be specific for orientation, while intracortical inhibitory connections appear to be non-specific in this respect. Experimental and theoretical studies have suggested that the development of cortical cell orientation tuning is an activity-dependent process.     

An incremental Hebbian learning model of the primary visual cortex with lateral plasticity and real input patterns

We present a simplified binocular neural network model of the primary visual cortex with separate ON/OFF-pathways and modifiable afferent as well as intracortical synaptic couplings. Random as well as natural image stimuli drive the weight adaptation which follows Hebbian learning rules stabilized with constant norm and constant sum constraints. The simulations consider the development of orientation and ocular dominance maps under different conditions concerning stimulus patterns and lateral couplings. With random input patterns realistic orientation maps with +/- 1/2-vortices mostly develop and plastic lateral couplings self-organize into mexican hat type structures on average. Using natural greyscale images as input patterns, realistic orientation maps develop as well and the lateral coupling profiles of the cortical neurons represent the two point correlations of the input image used.     

Horizontal organization of orientation-sensitive cells in primate visual cortex

In the visual cortex of the monkey the horizontal organization of the preferred orientations of orientation-selective cells follows two opposing rules:(1) neighbors tend to have similar orientation preferences, and(2) many different orientations are observed in a local region. We have described a classification for orientation maps based on the types of topological singularities and the spacing of these singularities relative to the cytochrome oxidase blobs. Using the orientation drift rate as a measure we have compared simulated orientation maps to published records of horizontal electrode recordings.     

Cortical bone remodeling rates in a sample of African American and European American descent groups from the American Midwest: comparisons of age and sex in ribs

This study employs regression analysis to explore population and sex differences in the pattern of age-associated bone loss, as reflected by histomorphometric variables that are measures of intracortical and endocortical bone remodeling. A comparison of an African American sample from the Washington Park Cemetery in St. Louis, Missouri, and a European American rib sample composed of cadavers, autopsies, and forensic cases from Missouri reveals the existence of complex age-associated patterns for differences in measures of intracortical remodeling and cortical area. Females from the two samples express similar bone dimensions and dynamics. The African American females appear to lose more bone than their male counterparts, but this difference is absent in the European American sample. When age-associated patterns are considered, it is in the younger cohorts that African Americans exhibit greater relative cortical area than European Americans, but this is reversed in the older ages, when the latter group manifests greater bone mass. The European American males consistently differ in the slopes and intercepts for the variables compared to the other groups, and differences are highly significant with African American females, with the former group maintaining bone mass while the latter exhibit a more rapid bone loss. Achieving larger relative cortical area due to smaller endosteal area, coupled with better bone quality due to lower intracortical porosity early in life, may be a mechanism by which African Americans, especially females, maintain adequate bone mass in older ages, which buffers them from bone loss and related fragility fractures despite higher rates of intracortical remodeling and endosteal expansion later in life. These results suggest that both genetic and environmental factors are responsible for the differences in bone remodeling and bone mass observed between these samples.     

Distinct cortical circuit mechanisms for complex forelimb movement and motor map topography

Cortical motor maps are the basis of voluntary movement, but they have proven difficult to understand in the context of their underlying neuronal circuits. We applied light-based motor mapping of Channelrhodopsin-2 mice to reveal a functional subdivision of the forelimb motor cortex based on the direction of movement evoked by brief (10?ms) pulses. Prolonged trains of electrical or optogenetic stimulation (100-500?ms) targeted to anterior or posterior subregions of motor cortex evoked reproducible complex movements of the forelimb to distinct positions in space. Blocking excitatory cortical synaptic transmission did not abolish basic motor map topography, but the site-specific expression of complex movements was lost. Our data suggest that the topography of?movement maps arises from their segregated output projections, whereas complex movements evoked by prolonged stimulation require intracortical synaptic transmission.     

Standing waves and traveling waves distinguish two circuits in visual cortex

The visual cortex represents stimuli through the activity of neuronal populations. We measured the evolution of this activity in space and time by imaging voltage-sensitive dyes in cat area V1. Contrast-reversing stimuli elicit responses that oscillate at twice the stimulus frequency, indicating that signals originate mostly in complex cells. These responses stand clear of the noise, whose amplitude decreases as 1/frequency, and yield high-resolution maps of orientation preference and retinotopy. We first show how these maps are combined to yield the responses to focal, oriented stimuli. We then study the evolution of the oscillating activity in space and time. In the orientation domain, it is a standing wave. In the spatial domain, it is a traveling wave propagating at 0.2-0.5 m/s. These different dynamics indicate a fundamental distinction in the circuits underlying selectivity for position and orientation, two key stimulus attributes.     

Neuronal selectivity and local map structure in visual cortex

The organization of primary visual cortex (V1) into functional maps makes individual cells operate in a variety of contexts. For instance, some neurons lie in regions of fairly homogeneous orientation preference (iso-orientation domains), while others lie in regions with a variety of preferences (e.g., pinwheel centers). We asked whether this diversity in local map structure correlates with the degree of selectivity of spike responses. We used a combination of imaging and electrophysiology to reveal that neurons in regions of homogeneous orientation preference have much sharper tuning. Moreover, in both monkeys and cats, a common principle links the structure of the orientation map, on the spatial scale of dendritic integration, to the degree of selectivity of individual cells. We conclude that neural computation is not invariant across the cortical surface. This finding must factor into future theories of receptive field wiring and map development.     

Dynamic modification of cortical orientation tuning mediated by recurrent connections

Receptive field properties of visual cortical neurons depend on the spatiotemporal context within which the stimuli are presented. We have examined the temporal context dependence of cortical orientation tuning using dynamic visual stimuli with rapidly changing orientations. We found that tuning to the orientation of the test stimulus depended on a briefly presented preceding stimulus, with the preferred orientation shifting away from the preceding orientation. Analyses of the spatial-phase dependence of the shift showed that the effect cannot be explained by purely feedforward mechanisms, but can be accounted for by activity-dependent changes in the recurrent interactions between different orientation columns. Thus, short-term plasticity of the intracortical circuit can mediate dynamic modification of orientation tuning, which may be important for efficient visual coding.